Quarter square electric voltage multiplier



Sept. 29, 1959 c. A. LOVELL QUARTER SQUARE ELECTRIC VOLTAGE MULTIPLIER Filed April 13, 1953 w lml. M E NV m WH0. .C l P L A wr a dm QI Q* o 'd NLN..

' on the algebraic identity;

QUARTER SQUARE ELECTRIC VOLTAGE MULTIPLIER Clarence A. Lovell, Summit, NJ., assi'gnor to Bell Telephone Laboratories, Incorporated, New York, N.Y., a corporation of New York Application April 1s, 1953, serial No.1's4s,z39

1 claims. (Cl. 23S-194) A basic feature of' this invention isa methodyof mul- Refer now to Fig. 1 of the drawing. In Fig. 1 an alternating-current voltage A is impressed on the primary of the transformershown at the upper leftr. The mid-point of the secondary winding is grounded; A voltage +A is produced in-,theupper winding of the secondarynand iinpressed on voltage summer 1, which is a device for suinming up a plurality of voltages. This device is well known in theart being disclosed, for instance, in Patent No.

2,408,081 granted to Lovell-Parkinson-Swartzel-Weber, September 24, 1946, and more particularly in Fig. 12v of said,Y patent. See' also Vacuum Tubes and Ampliers, Radiation Laboratory Series, vol. XVIII by McGraw-Hill Book Company 1948, edited by Valley and Wallman; and Electronic Instruments, Massachusetts Institute of Technology, Radiation'rLaboratory Series,y vol. 21, McGraw- Hill Book Company 1948, Greenwood, Holdam and Mac- Rae, page 32.

` The voltage +A is also applied to the input vof an identical voltage summer, voltage summer 2. The alternatingcurrent voltage B is impressedv on the primarylof the Y transformer shownat the lower left in the drawing, the

tiplying voltages; more accurately expressed perhaps, a

method of causing equipment to produce a voltage'which is at least-va close approximation to the product of two applied voltages. f

A feature of'theinvention is an electronic voltage multiplier which may be used, for example, in a, system of electrical transmission Vdisclosedin'Patent No, 2,658,189, issued' November 3, 1953 upon the"application 'above identified. The electronic voltage multiplier`may-beap plied generally wherever there is need of multiplying voltages and comprises one species of apparatus for executing the method. The voltages Lwhich Imaybe multiplied-may be either direct-current voltages orl alternating-current voltages; y

The invention may be understood from the 4following description when read with.referenc'e to the associated drawingin whichzi Y i Fig. l shows acircuit for 'multiplying alternating-currentvoltagesand"`r Y l Fig. 2` shows a circuit for multiplying direct-current voltages. i

The circuit o f Fig. 1 herein corresponds to the circuit of Fig. 3 of the application identiiied-in the foregoing.

Electronic multiplier l Most modulators are approximate multipliers in which f rthe pure product, although not accurately scaled, is included among the outputs.v For most purposes they are made satisfactory through the process of using frequency selective networks to-'passthe desired produ'ctandy to ex- A cludeall other terms which Aappear inthe output. Y

The present inventionV is a method of electronic multiplication which involves a voltage a'ddepforvoltage summer, as itis sometimes called, and a non-linear element. The element is chosen so thatit hassubstantially. a square law characteristic,-so thatthemultiplication-,is substantially precise.l

The operation of the .circuit of the `drawing is# based Adding (a) and (b) +B is applied to the input of the voltage summerl and the'voltage -B is applied to the input ofthe voltage summerl 2. Thus, voltage +A and voltage +Bv areiapplied tothe input of voltage summer l and voltage +A and voltagey -B are yapplied to the input of voltage summer 2. Voltage A+B isk produced across the secondary of the transformer connected to the output of voltage summer l andthe voltage A-B is produced4 across the secondary of the transformer connected to the output of voltage summer 2. These voltages A+B and A-B are each applied to the input of an4 individual non-linearv conducting deviceselected to have a square law characteristic', a numberzof which are Well yknown in the art. This serves as a` voltage squarer. The output of each voltage squaring devicefis impressed across an individual potentiometer. The polarities of the non-linear elements as disposed in v.the voltage squarers are arranged so that the .polarities ofthepotentials across theipotentiometers,are reversed, one with respect to the other. The associated sliding contact is adjusted to provide a voltage of positive 1A (A+B)2vfrom the upper potentiometer and'negative1/4 (A 13)2 from the lower potentiometenf, These twovoltages; are impressed on the input of voltage summer 3,V

-Squaring each of the sums i l A2 221BL B2 TLT A2 ZAB- B2 t+1-Tf y +AB v. 7 Nolcircuit elements 'are available in which the outputs E'o are related' to the input E, precisely by the relation atented Sept. 29, 1959 .reverse the polarity of the Vadded voltages.

where 'krisa constant. However a large number of elements are found having substantially-this-response. The utilization of such elements as square law detectors, such as described herein, is well known inthe art, as illustrated in Torrey and`Whitmer,Crystalletiiies, 15 M-I'TJI'Radiation -LaboratorieslSeries 3,333 (flvfrldc1948i)- 'The present'fullwave rectification circ with-'a'voltagef'divider` output, permits adjustments to improve the approximations inherentfin such elements. Typicalyofsuch vadjustments arethose 1which maybern'ade' tcyniakeitheY "out`A put ero `when one` of the inputs V'isrnade"2i e`ro"orfone which will make the'output precisewhnAandB arefse't in Igiven values. m l g `For l the 'non-linear elements, "copper toxide, ''vacu'ur'n tubes and yso or'thjoier fairly-goodapproximations` over limited ranges. Thus,y the ycircuit-"of Ythe Y drawir'lgl inayl'be constructed-from conventional components. Y

`Inthe arrangement show'n'dn ther'ircitper -Fig. l, the 4voltages A 4and B as'nent'iond `are 'alternatingcurrent voltages and arefshown as lapplied through transformers. w

ReferV now to Fig. 2 which 'showsi'a' circuit -for` multiplying two' direct-current -voltagcs'fA and" B. The circuits per Figfl and Fig. 2 functionally, yand withffrespect to the 'apparatus elements employed, are `essentially 44the s'a'me, in that'they both vperform multiplication by "implementing the'operationsimplicit 4in Ythe algebraic formulas presented in`theforegoingand they both :employ circuits similarly arranged and *having Avoltage summers, vltage squarers and 4voltage I quarter-ersv disposed i lin Ithe same manner. One -impcr rtat1tfdiierc'fncei Lis fin thefg'rounding arrangements. Other"`differences areuthat in'Fig. v2"'an electronic` device, `voltage plarityj' inverter "1,51is` 4'indicated for reversing'jthepol'arity of vdltagerB Iand another, voltagegpolarity inverter 2, or'reve'rsing'the polarity ofthecmtputof` voltage summer-3D. -It willbeob served `that ina'direct'`cu1rent circuit the'polarty 'of "the output ofthe VSumrr'iers'is the" opposite Vfrom that vof the input. 'l'trjwill'befobservedalso that thepolarity of4 the output ofjeachof'the summers 1D vand 2D is negative.

v Fig. 2'shows in detail'the manner inwhich the polarityfof the out-putY of two squaring devices 'may be reversed one :with respect tothe other. lt will beobserved thaty thefpolarity pf each dry rectifier' element "of 'rectierw 2 has `polarity lreversed with respect tovv each corresponding Adry rectifier; element 'of rectiiierl. The elements .asytlius Vdisposed aiord a `path for thenegative potential'applied to the' respectivetop` terminalsjof :the rectifier-s, I In the'fcase o'f rectifier 1 thecircuit extends fromy the "top vterminal ofv rectiiier .1 through rectier `element' a; potentiometer P1 and rectiiier element b'to jgroun d The bottom 'terminal of potentiometer P1 'is .negative with'respect to itsupper'terminal. n Por rectifier 2'the path "forinegative potential applied to'itstop -terminal is through rectier c, potentiometer `-P2 :and lrectifier d to ground, so that the polarityof the V4topterminal of potentiometer P2 is negative -with respectito its'flower terminal. Therefore, the polaritiesof 'the potentials between the slider of each potentiometer and the common lead forming the input to voltage summer 3D will`b'e positive from potentiometer P1 and negative from potentiometer P2.

The voltage summer 3D' will add these voltages and This gives the negative product of voltage A and voltage B as a result. This negative product is inverted in jvoltage polarity inverter 2 to afford the positive desired product voltage AB. 'fr

What is claimed is z' 1. A voltage multipliergsaid multiplier comprising a first summing device for adding voltages A and B, a second summing device for adding voltage A and voltage --B, a first fsquarejlaw element which substantially squareslvoltage v CA+B -),a j second square law element which substantially squares voltage (AB), means for reversing the polarity of one of said squared voltages with respect tothe other, rmeans for quartering each .of said squared voltages, one having its sign so reversed, and a third summing device for adding said quartered voltages to provide a voltage substantially equal to the product of voltage A and voltage B.

2. Apparatus for multiplying-electrical voltages A and B comprising .means vfor impressing voltages +A and +B upon 'the input of aflirst .electronic voltagesummer to produce voltage (A +B) Yin vthe output of said voltage summer, .means Ifor impressing lvo'ltages +A and -B upon the input of a secondelectronic voltage summerto produce voltage (A-B) in Vthe -output of'said second voltage summer, a first voltage -squaring element for squaring voltage (A+B), a second voltage squaring element for squaring -voltag'e- (A+B), means for reversing the sign of the polarity of one of said squared voltages with respect to the other, a rst voltage quartering devi'cefor Vquartering one ofsaid squaredv voltages,:a"sec ond svoltagc quartering :device -for `quartering y'the other of saidsquared voltages having lits Vsignso changed and a third lelectronic voltage summer for 'adding 'said :quartered `v'nltages ito obtain 'a' 'voltge'equal to therproduct of :voltage A and voltage B.

"3.1'Inran :electrical circuit,4 a firstcircuitbranch, a first non-linear element having a substantially square law characteristic fin`ssaid branch, fa 'rstfrpotentiometer connected -zto l:said :non-linear element, -a -second -circuit branch in parallel with said lirst'circuit'branch,a second non-linear element having :a zsubstantially square law characteristic in said second branch, a second potentiometer connectedjto said 4second nonalinear element, a common circuit path having a potential responsive device v connected to veach :of said .potentiometers, and .instru- 35 mentalities in .said `nonelinear elements forreversing the polarity `ofone t of the ,potentials derived Ifrom oneof -said potentiometers with ,respect to the .otherof said potentials derived from the other of said potentiometers.

4. An electrical circuit-for multiplying two direct- 'current'l voltages, voltage +A and voltage +B, to obtain voltage AjB, said circuit having a irst and a second branch connected in parallelrsaid branches connected to a third .common `series branch, a iirst voltage summer, a yrst square vlaw element and a rst potentiometer connected inser'ies'injfsaid rst branch, a irst voltage polarity in- .verter, xav'second voltage summer, ia second square law element and Va second potentiometer vconnected yin series in said second branch, a third voltage summer and a sec- 4ond voltage polarity `inverter connected sequentially in tseries Vin said third branch, means for impressing said voltage +A and said voltage +B on saidnrst voltage .summer and means -responsive thereto for producing a voltage -(A+B), means for impressingfsaidfvoltage --1(A-+B) Non said iirst square law element and rsaid tirst 55 potentiometer and means responsive thereto for produczingfa voltage y+111(A-l.l3.')2, -meansA n-for impressing said voltage +B on said rst voltage polarity inverter and means responsive thereto for producing a voltage -B, means for impressings'aid voltages +A and -B on said ysecond voltage summer and `means responsive thereto for producing a voltage (A+B.) means for impressing said -Noltage -.(.A-B) on said second square -1aw element and fsaid 'second potentiometer andA means responsive -thereto :for fproducing a voltage -IA (Aa-B)2,-means for 65 impressingzsaid voltages -|-%.'(A+B;)2 fand 1A (fi-B)2 olifsaid'rthird yvoltage summer and means responsive there- -to for iproducing'ra' voltage Y-AB, .means for vimpressing .said voltage -A-B ionxsaid second voltage polarity in- .'verter, andmeansV fresponsive ttheretofor producing a voltage +AB, reach'of said square tlaw 'elements-:a bridge having four arms and a dry rectifier in eachfof'said arms, each d'ry rectifier in each "of .said arms :of said second square law element having itsf'polanity-zre'versed `with respect to each dry rectifier in the corresponding arm of 75 said first square law telement.

5. An electrical circuit for multiplying two alternating voltages, voltage +A and voltage +B, to obtain voltage H-AB, said circuit comprising a source of voltage A connected to the input of a first transformer, the output of said rst transformer connected in parallel to a iirst voltage summer in a irs't parallel circuit branch and to a second voltage summer in a second parallel circuit branch, a source of voltage +B connected to the input of a second transformer, the output of said second transformer having two windings with a common terminal grounded, means for producing a voltage ,+B and -B in the output of said second transformer, means for impressing said voltage +B on the input of said iirst voltage summer, means for impressing said voltage -B on the input of said second voltage summer, a'rst square law element connected to the output of said first voltage summer, a first potentiometer connected to the output of said rst square law element, a second square law element connected to the output of said second voltage summer, a second potentiometer connected to the output of said second square law element, the output of said iirst potentiometer and of said second potentiometer connected in parallel to the input of a third voltage summer, means responsive to the impressing of said voltages +A and +B on said rst voltage summer for producing a voltage +(A+B), means responsive to the impressing of said voltage +(A+B) on said iirst square law element for-producing a voltage +(A+B)2, means for adjusting said first potentiometer to produce a voltage +1A (A+B)2, means responsive to the impressing of said voltages +A and -B on said second voltage summer for producing a voltage +(A-B), means responsive to the impressing of said voltage +(A-B) on said second square law element for producing a voltage +(A-B)2, means in said second potentiometer for producing a voltage -l/4 (A-B)2, and means in said third voltage summer responsive to the impressing thereon on said voltages +%(A+B)2 and -Mt (A--V for producing a voltage AB. t

6. An electrical circuit having inputs to first and second parallel circuit branches, each of said branches comprising in series, an individual voltage summer, a rectiiier bridge circuit having four arms, each arm having a square law dry rectier element therein, an individual voltage divider, and means for reversing the polarity of the output of one of said branches with respect to the polarity of the output of the other; said parallel branches connected in series with a single voltage summer in a common circuit. t

7. A circuit in accordance with claim 6 having a voltage polarity inverter connected to the output of said single voltage summer in said common circuit.

References Cited in the tile of this patent UNITED STATES PATENTS 2,059,594 Massa Nov. 3, 1936 2,196,996 Lang Apr. 16, 1940 2,401,447 Wipi June 4, 1946 2,408,081 Lovell et al Sept. 24, 1946 2,428,541 Bagley Oct. 7, 1947 2,441,387 Berger et al May 11, 1948 2,454,549 Brown et al Nov. 23, 1948 2,587,193 Miller Feb. 26, 1952 OTHER REFERENCES 

